1. Sequences, Series and the test of their convergence
Chapter 1
Sequences, Series and the test of their convergence
Lectures 3, 4 and 5: Series and convergence
Understand the definition of a convergent infinite series.
Use properties of infinite geometric series.
Use the nth-Term Test for Divergence of an infinite series.
Calculus for engineers
MATH Level 3
Haykel MAROUANI
Office F093

2. Haykel MAROUANI (hmarouani@ksu.edu.sa)
Sigma notation 
Haykel MAROUANI
Office F093

3. Haykel MAROUANI (hmarouani@ksu.edu.sa)
Infinite series
One important application of infinite sequences is in representing “infinite summations”. If {an} is an infinite sequence, then
is an infinite series (or simply a series). The numbers a1, a2, a3, … are the terms of the series. For some series it is convenient to begin the index at n=0 (or some other integer). As a typesetting convention, it is common to represent an infinite series as Simply an. In such cases, the starting value for the index must be taken from the context of the statement.
Haykel MAROUANI
Office F093

4. Calculus for engineers
Example 1
Calculus for engineers
MATH Level 3
Haykel MAROUANI
Office F093

5. Calculus for engineers
Geometric series
The series given by
is a geometric series with ratio r.
Example 2
Calculus for engineers
MATH Level 3
Haykel MAROUANI
Office F093

6. Calculus for engineers
nth-Term test for divergence
Example 3
Calculus for engineers
MATH Level 3
Haykel MAROUANI
Office F093

7. Calculus for engineers
p-series and harmonic series
Calculus for engineers
MATH Level 3
Haykel MAROUANI
Office F093